# The Dirichlet Boundary Value Problem in Strongly Perforated Domains with Complex Boundary

Chapter

## Abstract

In this chapter, we study the asymptotic behavior of solutions of the Dirichlet problem in domains ω^{(s)}=ω/*F*^{ (s) }, where ω is some fixed domain in ℝ^{ n } (*n*≥2) and *F*^{ (s) } (*s*=1, 2,…) are arbitrary closed sets. In contrast with the preceding chapter, where the sets *F*^{ (s) }=U _{ i=1 } ^{s} *F* _{i} ^{(s)} consisting of disjoint components *F* _{i} ^{(s)} , “grains,” have been considered, here the main attention is focused on connected sets *F*^{ (s) }. Typically, such sets consist of thin (generally, intersecting) fibers forming weblike structures.

## Keywords

Variational Problem Dirichlet Problem Weak Limit Orlicz Space Complex Boundary
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## Copyright information

© Birkhäuser Boston 2006